Half space representation of a convex polytope

Question

We know that the half space representation of a polytope is given by: $Ax<b$.
Consider a convex polytope in $\mathbb{R}^3_+$ with vertices given by the following set of points: $\left\{(0,0,0),(1,0,0),(0,1,0),(0,0,1),(0.8,0.8,0),(0.8,0,0.8),(0,0.8,0.8),(0.7,0.7,0.7) \right\}$.
How can we find the half space representation of this polytope?
My goal is to learn the method and try to apply it for higher dimensions.